01:29:
In circle o, the length of radius OL is 6 cm and the length of
arc LM is 6.3 cm. The measure of angle MON is 75°.
Rounded to the nearest tenth of a centimeter, what is the
length of arc LMN?
6.3 cm
6 cm
7.9 cm
10.2 cm
12.6 cm
14.2 cm

The length of arc LMN is 14.2cm

Step-by-step explanation:

First of all we have to calculate the circumference of the circle and then extract the portion that corresponds to MN

To solve this exercise we need to use the circumference formula of a circle:

c = circumference

r = radius = 6cm

π = 3.14

c = 2π * r

we replace the known values

c = 2 * 3.14 * 6cm

c = 37.68cm

As we know a circle is represented with 360 ° and they tell us that the angle of the MN part is 75 °, so we have to know the relationship with respect to the total

75° / 360° = 5/24

Now we multiply this number by the circumference and we will obtain the length of the arc MN

MN = 37.68cm * 5/24

MN = 7.85cm

Now we add the values of LM with NM and we will obtain the length of LMN

LMN = 6.3cm + 7.85cm

LMN = 14.15cm

round to the nearest tenth

LMN = 14.15cm = 14.2cm

The length of arc LMN is 14.2cm